Longevity hedge effectiveness: A decomposition

We use a case study of a pension plan wishing to hedge the longevity risk in its pension liabilities at a future date. The plan has the choice of using either a customised hedge or an index hedge, with the degree of hedge effectiveness being closely related to the correlation between the value of the hedge and the value of the pension liability. The key contribution of this paper is to show how correlation and, therefore, hedge effectiveness can be broken down into contributions from a number of distinct types of risk factors. Our decomposition of the correlation indicates that population basis risk has a significant influence on the correlation. But recalibration risk as well as the length of the recalibration window are also important, as is cohort effect uncertainty. Having accounted for recalibration risk, additional parameter uncertainty has only a marginal impact on hedge effectiveness. Finally, the inclusion of Poisson risk only starts to become significant when the smaller population falls below about 10,000 members over age 50. Our case study shows that, at least for medium and large pension plans, longevity risk can be substantially hedged using index hedges as an alternative to customised longevity hedges. As a consequence, when the hedger's population involves more than about 10,000 members over age 50, index longevity hedges (in conjunction with the other components of an ALM strategy) can provide an effective and lower cost alternative to both a full buy-out of pension liabilities or even to a strategy using customised longevity hedges

Three retirement decision models for defined contribution pension plan members: A simulation study

This paper examines the hypothetical retirement behavior of defined contribution (DC) pension plan participants. Using a Monte Carlo simulation approach, we compare and discuss three retirement decision models: the two-thirds replacement ratio benchmark model, the option-value of continued work model and a newly-developed "one-year" retirement decision model. Unlike defined benefit (DB) pension plans where economic incentives create spikes in retirement at particular ages, all three retirement decision models suggest that the retirement ages of DC participants are much more smoothly distributed over a wide range of ages. We find that the one-year model possesses several advantages over the other two models when representing the theoretical retirement choice of a DC pension plan participant. First, its underlying theory for retirement decision-making is more feasible given the distinct features and pension drivers of a DC plan. Second, its specifications produce a more logical relationship between an individual's decision to retire and his/her age and accumulated retirement wealth. Lastly, although the one-year model is less complex than the option-value model as the DC participants' scope is only one year, the retirement decision is optimal over all future projected years if projections are made using reasonable financial assumptions.Defined contribution pension plan Dynamic and stochastic simulation One-year retirement decision model Two-thirds model Option-value of continued work model

Longevity risk and the Grim Reaper's toxic tail: The survivor fan charts

This paper uses survivor fan charts to illustrate the prospective density functions of future male survival rates. The fan charts are based on a version of the Cairns-Blake-Dowd model of male mortality that provides a good fit to recent mortality data for England and Wales. They indicate that although none of us can escape the Grim Reaper, survivorship uncertainty is greatest for males aged a little over 90, confirming that there exists a [`]toxic tail' for those institutions, such as annuity and pension providers, which are obliged to make payments to them for as long as they live. We also find that taking account of uncertainty in the parameters of the underlying mortality model leads to major increases in estimates of the widths of the fan charts.